I've had my tonsils removed a long time ago. I'm facing difficulty in pronouncing some sounds that start in throat like the french R. Does the lack of tonsils make it impossible for me produce the correct sound?
No, the tonsils aren't involved in the production of a voiced uvular fricative (what is the linguistic term for the French r). So, even without tonsils most people can produce this sound. Tonsil extraction is a frequent surgical treatment and does not cause speech impediments (usually, rare effects may be there or not, I have no information on that).
EDIT: In the first writing, I assumed that the French r were an uvular trill—it nowadays usually isn't. The Wikipedia article Guttural R has an overview on different realisations of the guttural r.